Two-tone Pinwheel

Geometry Level 5

In a quadrilateral ABCDABCD in which ABD=BDC=40\angle ABD=\angle BDC=40^\circ and BCA=CAD=45 \angle BCA=\angle CAD=45^\circ, find the smaller of the two angles between the diagonals.

Report the positive difference between the two solutions to this problem.

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